We accommodate potentially noisy annotations by providing soft bounds for the local scales, allowing the adaptation of incorrect signals given sufficient evidence from the data.
Experiments show that a slab width of \(c_{g, k} \approx 1.0\)  for genes annotated to a pathway and \(0 < c_{g, k} < 0.1\)  for unannotated genes provide the best results.
We assign a relatively large slab width across all genes for the unannotated dense factors, and vice-versa for the unannotated sparse factors, allowing the model to autoregulate active signals based on the data.
Alternative implementations of sparse factor analysis models rely on the spike-and-slab prior [1]}, [2]}; however, due to their discrete nature, these models cannot be trained using blackbox stochastic variational inference and therefore tend to be inefficient.
We implement the alternative parameterization of the regularized horseshoe as suggested in [3]} and described above. The resulting algorithm is amenable to efficient and scalable stochastic variational inference[4]}, [5]}, [6]}, and optimizes the evidence lower bound via standard gradient methods such as Adam[7]}.
